Problem: Simplify; express your answer in exponential form. Assume $p\neq 0, q\neq 0$. $\dfrac{{p^{-4}}}{{(p^{-1}q^{-5})^{-5}}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${p^{-4}}$ to the exponent ${1}$ . Now ${-4 \times 1 = -4}$ , so ${p^{-4} = p^{-4}}$ In the denominator, we can use the distributive property of exponents. ${(p^{-1}q^{-5})^{-5} = (p^{-1})^{-5}(q^{-5})^{-5}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{p^{-4}}}{{(p^{-1}q^{-5})^{-5}}} = \dfrac{{p^{-4}}}{{p^{5}q^{25}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{-4}}}{{p^{5}q^{25}}} = \dfrac{{p^{-4}}}{{p^{5}}} \cdot \dfrac{{1}}{{q^{25}}} = p^{{-4} - {5}} \cdot q^{- {25}} = p^{-9}q^{-25}$.